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Models of G–spectra as presheaves of spectra

https://doi.org/10.2140/agt.2024.24.1225

Guillou, Bertrand J; May, J Peter (January 2024, Algebraic & Geometric Topology)
Greenlees, John (Ed.)
Let G be a finite group. We give Quillen equivalent models for the category of G–spectra as categories of spectrally enriched functors from explicitly described domain categories to nonequivariant spectra. Our preferred model is based on equivariant infinite loop space theory applied to elementary categorical data. It recasts equivariant stable homotopy theory in terms of point–set-level categories of G–spans and nonequivariant spectra. We also give a more topologically grounded model based on equivariant Atiyah duality.
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The homotopy of the $$KU_G$$-local equivariant sphere spectrum

https://doi.org/10.1007/s40062-023-00336-z

Carawan, Tanner N; Field, Rebecca; Guillou, Bertrand J; Mehrle, David; Stapleton, Nathaniel J (December 2023, Journal of Homotopy and Related Structures)

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Multiplicative equivariant K-theory and the Barratt-Priddy-Quillen theorem

https://doi.org/10.1016/j.aim.2023.108865

Guillou, Bertrand J.; May, J. Peter; Merling, Mona; Osorno, Angélica M. (February 2023, Advances in Mathematics)

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An $$R$$-motivic $$v_1$$-self-map of periodicity $$1$$

https://doi.org/10.4310/HHA.2022.v24.n1.a15

Bhattacharya, Prasit; Guillou, Bertrand; Li, Ang (January 2022, Homology, Homotopy and Applications)

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$$C_2$$-equivariant and $$\mathbb {R}$$-motivic stable stems II

https://doi.org/10.1090/proc/15167

Belmont, Eva; Guillou, Bertrand J.; Isaksen, Daniel C. (January 2021, Proceedings of the American Mathematical Society)
null (Ed.)
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The Bredon-Landweber Region in C2-Equivariant Stable Homotopy Groups

https://doi.org/10.25537/dm.2020v25.1865-1880

Guillou, Bertrand J; Isaksen, Daniel C. (January 2020, Documenta mathematica)
null (Ed.)
We use the C2-equivariant Adams spectral sequence to compute part of the C2-equivariant stable homotopy groups π^{C2}_{n,n}. This allows us to recover results of Bredon and Landweber on the image of the geometric fixed-points map π^{C2}_{n,n}→π_0. We also recover results of Mahowald and Ravenel on the Mahowald root invariants of the elements 2^k.
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The cohomology of C2-equivariant 𝒜(1) and thehomotopy of koC2

https://doi.org/10.2140/tunis.2020.2.567

Guillou, Bertrand J.; Hill, Michael A.; Isaksen, Daniel C.; Ravenel, Douglas Conner (January 2020, Tunisian Journal of Mathematics)

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Enriched model categories in equivariant contexts

https://doi.org/10.4310/HHA.2019.v21.n1.a10

Guillou, Bertrand; May, J.P.; Rubin, Jonathan (January 2019, Homology, Homotopy and Applications)

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A symmetric monoidal and equivariant Segal infinite loop space machine

https://doi.org/10.1016/j.jpaa.2018.09.001

Guillou, Bertrand; May, J. Peter; Merling, Mona; Osorno, Angélica M. (June 2019, Journal of Pure and Applied Algebra)

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Categorical models for equivariant classifying spaces

https://doi.org/10.2140/agt.2017.17.2565

Guillou, Bertrand; May, Peter; Merling, Mona (January 2017, Algebraic & Geometric Topology)

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